Time Dilation and Relative Time

I was reading in Clifford M.Will's book "Was Einstein right? Putting General Relativity to the Test" that there was an experiment done where in October 1971 an experiment was done with radioactive clocks, and plane trips taken going with the spin of the earth, and against it. He reports: "The eastward trip took place between October 4 and 7 and included 41 hours in flight, while the westward trip took place between October 13 and 17, and included 49 hours in flight. For the westward flight the predicted gain in the flying clock was 275 nanoseconds (billionths of a second), of which two-thirds was due to gravitational blue shift; the observed gain was 273 nanoseconds. For the eastward flight, the time dilation was predicted to give a loss larger than the gain due to the gravitational blue shift, the net being a loss of 40 nanoseconds, the observed loss was 59 nanoseconds".

I understood him to have explained previously that with special relativity things moving relative to you (or any other frame of reference) will undergo time dilation relative to that reference. That the reference used was an imaginary clock in the centre of the earth, and the time dilation for the clock on the earth, and the clock in the plane being calculated relative to it. When going with the spin of the earth, the clock on the plane is moving faster relative to the imagined stationary clock in the centre of the world, than it is when it flies against the spin of the earth. So the eastward trip would show more of a time slow for the plane relative to the earth (which moves the same speed relative to the centre of the earth in both trips), and in the experiment while travelling against the spin time was gained (time was going faster), when travelling with it time dilation incurred countered the gain from less gravity to give an observed loss (the time dilation was seen).

What I don't understand is this can happen and time be relative. To hopefully make the problem in understanding it that I have more clear, imagine we performed 2 thought experiments, and in each we removed the planet, so we could ignore general relativity and just look at the special relativity aspect. Imagine that we just had the clock that was previously in the plane and the clock that was previously on the ground. Now relative to each other they could move as they did in the experiment in the with the spin leg. Now if things could be looked at relatively, I'd be assuming that in the first thought experiment we could imagine that the stationary point of reference was the clock that was on the ground in the experiment. We could see the two clocks together at the start, the 2nd clock leave the frame of reference and move relative to it before returning to the same frame of reference. I was thinking that since the 2nd clock would be moving relative to the first, actual time dilation for it would be expected. So it would lose time relative to the clock that was being considered to the first clock that we are imagining to be stationary. However I'm not sure why we couldn't we also have considered a different thought experiment in which we consider the 2nd clock to be the stationary frame of reference, and there the 1st clock would move relative to it, and there would be time dilation for the 1st clock, and so at the end the 1st clock would have lost time relative to the stationary 2nd clock. I guess I'm wrong because otherwise it would seem to me that the time dilation in the plane experiment showed which clock was moving relative to which (the clock in the plane underwent the time dilation relative to the clock on the Earth's surface because it was moving relatively faster), and therefore motion wouldn't be relative, and therefore nor would the time dilation.

As you can probably see, I'm slightly confused on the issue, and would appreciate any help on the matter.

What you have described is called the Twins Paradox.
Put more simply, consider two observers moving with respect to each other.
Each observer looks at the other's clock and observes the other clock is slow.
This is not a problem... it is similar to how two observers separated by a distance each observe the other to be short.
We call this second thing "perspective", and we are used to it so it does not seem strange.

"When our heroes meet again, what do they find? Did time slow down for Stella, making her years younger than her home-bound brother? Or can Stella declare that the Earth did the travelling, so Terence is the younger?

Not to keep anyone in suspense, Special Relativity (SR for short) plumps unequivocally for the first answer: Stella ages less than Terence between the departure and the reunion.

Perhaps we can make short work of the "travelling Earth" argument. SR does not declare that all frames of reference are equivalent, only so-calledinertial frames. Stella's frame is not inertial while she is accelerating. And this is observationally detectable: Stella had to fire her thrusters midway through her trip; Terence did nothing of the sort. The Ming vase she had borrowed from Terence fell over and cracked. She struggled to maintain her balance, like the crew of Star Trek. In short, she felt the acceleration, while Terence felt nothing.

Whew! One short paragraph, and we've polished off the twin paradox. Is that really all there is to it? Well, not quite. There's nothing wrong with what we've said so far, but we've left out a lot. There are reasons for the popular confusion."

Then it goes onto declare that according to Terrance the thing took 14 years and a day, and according to Stella 2 years, but I'm not sure how they got there.

Say there is A and B, they move apart and come back again, A claims that B was moving and that A was stationary, B claims that A was moving and B was stationary. How to tell which one was right, and which gets the slower clock is what I'm not sure about. I mean I can understand being able to say which one gets the time dilation if you knew whether either A or B's claim was right, but without knowing it (if both claims could be said to be equally as valid), how can you tell?

Twins paradox is the special case where the two observers meet again.
To do that, there must have been some accelerating... which means that SR no longer applies.
However it is possible to make headway using the tools of SR.

Basically: it is not a matter of who was really moving... such questions are meaningless.

Basically, Alice and Bob will agree about the final outcome, but disagree about hoe it came about. (Though they can resolve their differences by applying some relativity.)

Lets say Alice sees Bob zip by, travel some disrance, turn around and come back. Bobs clock is slow, so it is no surprise that Bob returns younger.

What Bob sees is this: Alice zips by, travels for some distance, then Bob exerts himself for a bit so that Alice turns around, and comes back.
The bit where Bob is using energy is where the outcome is decided for Bob.
On the outbound and inbound legs, Alice's clock is slow, but while turning around, her clock goes really fast.

I'll take a look at the paper thank you. Though your answer had some points that looked interesting.

Say there is A and B and they separate and come back again. Let us say that the gap between them increases exponentially by one hundredth the distance light would have travelled in a second, each second, for 5 seconds, so that the gap is 0.15 of a light second before continuing to increase at 0.5 of a light second for 3 seconds (I don't think this 3 seconds wouldn't require an accelerating frame), before increasing at 0.25 of a light second for 1 second, then decreasing by 0.25 of a light second (possibly a turn around like in the twin paradox), and continuing to decrease in a fashion opposite to the increase until they are at rest with one another again.. Now during any acceleration I understand that you're saying that SR wouldn't be appropriate, and I'd read on the twin paradox page I quoted earlier that for acceleration a psuedo magnetic field is added, and presumably this slows time as gravity does in general relativity. Though would you be saying that with the plane experiment, the slowing of time was done only during the moments of acceleration, because I was thinking that they were saying that some of the difference in the clocks was due to time dilation. If so then there would be some slowing of time in the period in between the acceleration(s) and deceleration(s). But which would get it A or B? Because when the clocks met up in the actual plane experiment one had it and the other didn't and in the book it was saying that SR was responsible for some of the difference. But if all frames of reference are equally valid, how can you tell whether A or B would get the type of time dilation they are saying they measured in the plane experiment. I was wondering if you could let me know what extra information you'd need to know before you could tell me whether A or B would have undergone the relative slowing of time because I can't see how you could do it from the information I have given you about A and B so far.

"When our heroes meet again, what do they find? Did time slow down for Stella, making her years younger than her home-bound brother? Or can Stella declare that the Earth did the travelling, so Terence is the younger?

Not to keep anyone in suspense, Special Relativity (SR for short) plumps unequivocally for the first answer: Stella ages less than Terence between the departure and the reunion.

You are misunderstanding the explanation. The unequivocal answer is that Stella ages less than Terence. That's not the same thing as saying that she is "really" moving. We can construct variants of the twin paradox in which both twins accelerate (the Hafele-Keating experiment you're asking about is like that) and ones in which neither twin accelerates. All of these variants work the same way: If you analyze them correctly using either the space-time diagram approach or the Doppler approach, you will find that in general the twins age by different amounts between their separation and their reunion.

Staff: Mentor

To do that, there must have been some accelerating... which means that SR no longer applies.

This is a very common misunderstanding. Special relativity works just fine in the presence of acceleration - google for "Rindler coordinates" for an example, and "relativistic rocket" for another.

Special relativity does not work in curved spacetime, which is to say in the presence of non-negligible tidal gravitational effects. That's what makes it "special" - it applies only to the special case of flat spacetime, whereas general relativity applies in the general case of flat or non-flat space-time. They're both perfectly comfortable with accelerations.

Well, the standard high school handwavey SR does not work for accelerating frames. You have to do something extra.
Rindler coords and such would, above, fall under "However it is possible to make headway using the tools of SR".
Its the sort of thing that tends to further confuse beginners... and we dont need it for the expaination above.

I the link that you gave I've read "Remember that relativity involves figuring out what an observation would seem like to one observer once you knew what it looked like to another observer who is moving with respect to the first" and that is something I haven't said in the A and B scenario. I assume A could say that B's sphere went away and came back, and that B could say that A's sphere went away and came back (maybe they are prisoners in spheres in space).

I wouldn't have thought it could be done from there either though, because if one report would be different from the other then how could they equally represent the non-moving frame. But maybe I'm missing something, or would more information be required?

Say there is A and B and they separate and come back again. Let us say that the gap between them increases exponentially by one hundredth the distance light would have travelled in a second, each second, for 5 seconds, so that the gap is 0.15 of a light second before continuing to increase at 0.5 of a light second for 3 seconds (I don't think this 3 seconds wouldn't require an accelerating frame), before increasing at 0.25 of a light second for 1 second, then decreasing by 0.25 of a light second (possibly a turn around like in the twin paradox), and continuing to decrease in a fashion opposite to the increase until they are at rest with one another again.. Now during any acceleration I understand that you're saying that SR wouldn't be appropriate,

The usual SR arguments you have been trying to use dont work during the acceleration.
The usual approach it to treat each velocity change as a shift from one inertial frame into another.
You example above just overcomplicates things. To see the details, simplify.

and I'd read on the twin paradox page I quoted earlier that for acceleration a psuedo magnetic field is added, and presumably this slows time as gravity does in general relativity.

Um.. whaa... off that I would recommend not using that page ever again. Just ignore it.
[edit]
The link you posted talks about "a pseudo gravitational field"... not magnetic.
It invokes the equivalence principle in GR, where uniform acceleration is indistinguishable from gravity. The author basically says that one party also undergoes a gravitational time dilation in addition to the usual one in SR. Since only one party accelerates, there is a difference in age.

Though would you be saying that with the plane experiment, the slowing of time was done only during the moments of acceleration,

No. Time does not slow down any more than distant objects get smaller.
Time dilation is a geometric effect that always happens.
Im saying that what determines the final outcome is the moments of acceleration.

there would be some slowing of time in the period in between the acceleration(s) and deceleration(s). But which would get it A or B?

Neither party gets slower time.
The party that ends up younger is the one that has the acceleration.
The reference I gave you has tools in ch1 to help you think about this.

Because when the clocks met up in the actual plane experiment one had it and the other didn't and in the book it was saying that SR was responsible for some of the difference. But if all frames of reference are equally valid, how can you tell whether A or B would get the type of time dilation they are saying they measured in the plane experiment.

In the standard examples one of the parties has undergone an acceleration. Thats how you tell.

I was wondering if you could let me know what extra information you'd need to know before you could tell me whether A or B would have undergone the relative slowing of time because I can't see how you could do it from the information I have given you about A and B so far.

You mean, which one ends up younger... time does not slow down for either of them... you are right, in your original example, you did not specify who did the accelerating. If you mean to describe a situation where A and B follow exactly symmetrical motions, then there will be no difference in their ages when they meet up.

Reread my description for Alice and Bob before... see how Bob has a different experience to Alice?
The reference I gave addresses your concerns. Please read before replying further to save typing.

You are misunderstanding the explanation. The unequivocal answer is that Stella ages less than Terence. That's not the same thing as saying that she is "really" moving. We can construct variants of the twin paradox in which both twins accelerate (the Hafele-Keating experiment you're asking about is like that) and ones in which neither twin accelerates. All of these variants work the same way: If you analyze them correctly using either the space-time diagram approach or the Doppler approach, you will find that in general the twins age by different amounts between their separation and their reunion.

Thank you for your help. Though and while I'm still confused, perhaps you could help me clear up my misunderstanding.

Imagine that there were two prisoners, prisoner A and prisoner B, both physicists. They are both in prison spheres which are equipped with telescopes, they are in the same rest frame and can see each other, but a gas is released from within the spheres, and they lose consciousness. When they wake up, using their telescopes they see that the distance between them is increasing at a fixed rate. They are gassed again, and when they wake up they see that they are travelling towards each other at a fixed rate. They are gassed again. And when they wake up, they are back next to each other again. How could they use SR to tell which of them had would undergo time dilation relative to the other, or would they need more information?

Imagine that there were two prisoners, prisoner A and prisoner B, both physicists. They are both in prison spheres which are equipped with telescopes, they are in the same rest frame and can see each other, but a gas is released from within the spheres, and they lose consciousness. When they wake up, using their telescopes they see that the distance between them is increasing at a fixed rate. They are gassed again, and when they wake up they see that they are travelling towards each other at a fixed rate. They are gassed again. And when they wake up, they are back next to each other again. How could they use SR to tell which of them had would undergo time dilation relative to the other, or would they need more information?

On the return journey they can tell which will end up younger... the one who accelerated while unconscious will be younger. This answer has already been provided in post #5... please reread, and check the reference I gave you... its a bit clearer than the references youve been using.
Note... both prisoners will observe time dilation. Neither will experience it.
"Time dilation" is the name given to the effect where observers in relative motion observe each other's clocks to run slow.

Concentrate on the simple situation in post #5 where one observer is accelerating.... can you not see that the two experiences are physically different?

There are multiple ways of "explaining" the twin paradox. I'll try one approach that I think might be helpful here. It considers an analog of the twin paradox, the "odometer paradox".

We know that a clock, moving a long a world-line, keeps a sort of time known as "proper time". And the "paradox" is that two clocks, taking different routes, show different readings when they meet up.

Let's consider the situation where we have, not clocks, but odometers, and the odometers move not through space-time, but through space. Then we know that the odometer measures the "length" of a path travelled through space.

We then construct the following "paradox". We have three points, A, B, and C. If you go from A to C, directly, you get one reading on your odometer, but if you go from A to B to C, you get a different reading. How is this possible?

Well, you probably don't even think there is a "paradox" there at all. But you can translate things that are confusing you about the Twin Paradox into the Odometer paradox, and gain some insight.

For instance, someone might ask "what is the mechanism that makes the path from A to C shorter than the path from A to B to C". You'd probably answer that the mechanism is geometry, or maybe more specifically, the triangle inequality.

Suppose someone asks "If you go from A to B to C, it's longer than going from A to C. How do you explain that if you go from A to C to B, that that is longer than going from A to B". You might say "It's the straight line distance that's always the shortest, and this is due to geometry".

Suppose someone objects to the abrupt change in direction you make when you turn, and insists that you had a car travel along the path from A to B to C, the car would need a curved road to be able to follow it. So you introduce a curve into the path (road) near B, to show that it doesn't make any difference, that the distance from A to B to C is still longer than the distance to A to C, that the curve makes the calculation a bit more complex, but it doesn't change the answer. Maybe, though, you get someone who is really obsessing about that curve, the one you put into the road at their request, who is asking how exactly this curve in the road. made the distance from A to C shorter. One answer might be that it's not the curve that makes the distance shorter, it's really the geometry. Translating this into the space-time version, the "curve" in the road is like the proper acceleration of some observer. And the "distance" is the proper time. So "the curve doesn't make the distance shorter, it's the geometry" translates into "the acceleration doesn't make the proper time longer, it's the geometry that does that".

Suppose someone has doubts that odometers are consistent, because they come up with different answers to distance depending on the path you take? You might reply - "well, that's just how they work, they behave in a consistent manner, you just have to understand them." The translation of this would be "The way time works in relativity is that clocks travelling along different paths read differently when the reunite, that's just how they work, they behave in a consistent manner, you just have to understand them".

I can't possibly come up with all possible objections one might have to clocks in relativity, but I've translated what I think is a reasonable sample into objections about clocks into objections about the behaviors odometers.

The abstract elements common to both odometers and clocks (which is the notion of curves , curves which have lengths) allow one to create useful analogies. One key element here is to point out that time and space are closely related in relativity, and that thinking about time in the way that one used to think about space can be productive.

Suppose someone objects to the abrupt change in direction you make when you turn, and insists that you had a car travel along the path from A to B to C, the car would need a curved road to be able to follow it. So you introduce a curve into the path (road) near B, to show that it doesn't make any difference, that the distance from A to B to C is still longer than the distance to A to C, that the curve makes the calculation a bit more complex, but it doesn't change the answer. Maybe, though, you get someone who is really obsessing about that curve, the one you put into the road at their request, who is asking how exactly this curve in the road. made the distance from A to C shorter. One answer might be that it's not the curve that makes the distance shorter, it's really the geometry. Translating this into the space-time version, the "curve" in the road is like the proper acceleration of some observer. And the "distance" is the proper time. So "the curve doesn't make the distance shorter, it's the geometry" translates into "the acceleration doesn't make the proper time longer, it's the geometry that does that".
.

You lost me there a bit, I wasn't thinking there was a curve between A and C I was thinking it was a straight line, the one with the curve (B was a curve on the A B C route) was longer. Also I'm not too clear on geometry even the 2D examples on surfaces seem to me to be 3d examples, where the extra dimensional information is held in the surface. I tend to think of it as Cartesian space, though I can understand that there is the idea that another spacial dimension exists the information about which is held in the 4D surface. But I find it hard to imagine. I appreciate all the effort, but it if you want to help if you could just explain this for me.

Imagine that there were two prisoners, prisoner A and prisoner B, both physicists. They are both in prison spheres which are equipped with telescopes, they are in the same rest frame and can see each other, but a gas is released from within the spheres, and they lose consciousness. When they wake up, using their telescopes they see that the distance between them is increasing at a fixed rate. They are gassed again, and when they wake up they see that they are travelling towards each other at a fixed rate. They are gassed again. And when they wake up, they are back next to each other again. How could they use SR to tell which of them had would undergo time dilation relative to the other, or would they need more information? Perhaps when there are two bodies in flat space time moving relative to each other, you need to know the history in order to know which one would undergo relative time dilation as described by SR? Or perhaps there would be certain geometry readings you would be looking for?

Staff: Mentor

In the intro it seems already to be settled that it Stella that was moving because of the acceleration, but that would mean that it isn't relative which one was moving.

You got it! Acceleration is not relative, so the twin that accelerates is the one that is "really" moving. Think about it this way: the one that accelerated had to fire-up a big rocket to do that. It doesn't make sense to say that you can fire a rocket engine and everyone else in the universe accelerates away from you as a result.

You got it! Acceleration is not relative, so the twin that accelerates is the one that is "really" moving. Think about it this way: the one that accelerated had to fire-up a big rocket to do that. It doesn't make sense to say that you can fire a rocket engine and everyone else in the universe accelerates away from you as a result.

Would thinking of it that way mean that motion may have a history involving acceleration, and that if so then it would have to be taken into account? If so then I guess that sorts out what your answer would be to the following: Imagine that there were two prisoners, prisoner A and prisoner B, both physicists. They are both in prison spheres which are equipped with telescopes, they are in the same rest frame and can see each other, but a gas is released from within the spheres, and they lose consciousness. When they wake up, using their telescopes they see that the distance between them is increasing at a fixed rate. They are gassed again, and when they wake up they see that they are travelling towards each other at a fixed rate. They are gassed again. And when they wake up, they are back next to each other again. How could they use SR to tell which of them had would undergo time dilation relative to the other, or would they need more information? When there are two bodies in flat space time moving relative to each other, do you need to know the history in order to know which one would undergo relative time dilation as described by SR?